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4 years ago

The explicit formula for a sequence is an=−2+3/2(n−1) What is the 21st term of the sequence?

Mathematics

1 answer:

Anni [7]4 years ago

8 0

Step-by-step explanation:

From the given question it appears that (n-1) is in the numerator's place, if it is so, then let us solve it.

$a_n = - 2 + \frac{3}{2}(n - 1) \\ \\ \therefore \: a_{21} = - 2 + \frac{3}{2} (21 - 1) \\ \\ \therefore \: a_{21} = - 2 + \frac{3}{2 } \times \: 20\\ \\ \therefore \: a_{21} = - 2 + 3 \times \: 10 \\ \\ \therefore \: a_{21} = { -2 + 30} \\ \\ \therefore \: a_{21} = 28 \\ \\ \huge \red{ \boxed{\therefore \: a_{21} = 28} } \\ \\$

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3 years ago

A distribution of values is normal with a mean of 220 and a standard deviation of 13. From this distribution, you are drawing sa

Paraphin [41]

Answer:

The interval containing the middle-most 48% of sample means is between 218.59 to 221.41.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributied random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 220, \sigma = 13, n = 35, s = \frac{13}{\sqrt{35}} = 2.1974$

Find the interval containing the middle-most 48% of sample means:

50 - 48/2 = 26th percentile to 50 + 48/2 = 74th percentile. So

74th percentile

value of X when Z has a pvalue of 0.74. So X when Z = 0.643.

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$0.643 = \frac{X - 220}{2.1974}$

$X - 220 = 0.643*2.1974$

$X = 221.41$

26th percentile

Value of X when Z has a pvalue of 0.26. So X when Z = -0.643

$Z = \frac{X - \mu}{s}$

$-0.643 = \frac{X - 220}{2.1974}$

$X - 220 = -0.643*2.1974$

$X = 218.59$

The interval containing the middle-most 48% of sample means is between 218.59 to 221.41.

5 0

4 years ago

Classify each triangle by its angles and by its sides.

MAXImum [283]

Answer:

Square is 90 degree angle

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

The perimeter of a rectangle is 234 meters.

Licemer1 [7]

I am going to show you how easy this is. Once you understand, you will be able to do this forever.

Assuming the side of the rectangle are (L) length and (W) width, the perimeter:

2L + 2W = 234

"the rectangle is twice as long as it is wide,", the equation for this statement:

L = 2W

In the first equation, we can replace L with 2W, then we have

2(2W) + 2W = 234

4W + 2W = 234

6W = 234

Divide both sides by 6

W = 234%2F6

W = 39 meters is the width

Remember it said the length is twice the width, therefore:

L = 2(39)

L = 78 meters is the length

Check this by finding the perimeter with these values

2(78) + 2(39) =

156 + 78 = 234

7 0

3 years ago

A scientist mixes water (containing no salt) with a solution that contains 35% salt. She wants to obtain 105 ounces of a mixture

Naya [18.7K]

Answer:

60 oz of water to add

45 oz of 35% salt solution should be used

Step-by-step explanation:

Let x = amt no. ounces in the first solution

and 105 - x = amt no. of ounces in the second solution

Ist solution contains 0% salt

2nd solution contains .35(105 - x) salt

.15(105= amt of salt in mix

So.

amt of salt in 1st solution + amt of salt in 2nd solution = amt of salt in the mix

0 + .35(105 - x) = .15(105)

Let's get rid of the fractions by multipying thru the equation by 100

35(105 - x) = 15(105)

3675 - 35x = 1575

-35x = -2100

x = 60 oz of water to add

105 - 60 = 45 oz of 35% salt solution should be used

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3 years ago